A267296 Circulant Ramsey numbers RC_1(3,n) of the first kind.

3, 3, 9, 14, 15, 22, 25, 34, 37, 46, 49

Offset

2,1

Comments

The smallest positive number a(n), such that any triangle-free cyclic (also known as circulant) graph with a(n) vertices has independence number at least n. The terminology and the terms given here are from Harborth and Krause.

a(n) <= A267295(n) for all n.

Moreover, the sequence is related to the ordinary two-color Ramsey numbers R(3,n), given in A000791, by the relation a(n) <= A000791(n) for all n, as proved by Kalbfleisch. This inequality is known to be an equality for n = 2 or 4 <= n <= 5.

References

H. Harborth, S. Krause, Ramsey Numbers for Circulant Colorings, Congressus Numerantium 161 (2003), 139-150.

Links

Table of n, a(n) for n=2..12.

Index entries for sequences related to Ramsey numbers

Crossrefs

Cf. A000791, A267295.

Sequence in context: A138383 A052436 A243790 * A122847 A197462 A264098

Adjacent sequences: A267293 A267294 A267295 * A267297 A267298 A267299

Keyword

nonn,hard,more

Author

Jörgen Backelin, Jan 12 2016

Status

approved